Hi,
What is the meaning to capture detail information in an image? What is image detail? Please ask me with an example.
This is good question with many possible answers, depending on a quite a number of things such as computational geometry, topology, mathematical analysis, algebra and statistics and probability theory in the analysis and representation of digital images.
One way to get started is to consider the pixels (picture elements) in a raster image. This is done, for example, using Navier-Stokes inpainting (see attached images: portrait, closeup of the eye with pixels inaccurately represented by tiny squares and eye image interpolation using Navier-Stokes inpainting) in
T. Wittman, Mathematical techniques for image interpolation:
http://www.math.ucla.edu/~wittman/thesis/Poral2.pdf
See Section 1.1, starting on page 2, for an introduction to the image interpolation problem. A good summary of the properties of an interpolated image is given on page 3. A good introduction to the statistical approach to image analysis is given in Section 6, starting on page 21.
Perhaps one of the most important studies of information in digital images was begun by A. Rosenfeld during the 1970s. It was Rosenfeld who introduced the notion of 8-neighbourhoods in digital images. Briefly, an 8-neighbourhood is defined by a particular pixel p and the 7 pixels adjacent to p. Rosenfeld's introduction of neighbourhoods of pixels ushered in the study of digital geometry and the digital topology of digital images. This subject is nicely introduced in
T.A. Aberra, Topology Preserving Skeletonization of 2D and 3D Binary Images, M.Sc. thesis, Technische Universitaet Kaiserlautern, 2004:
http://www.itwm.fraunhofer.de/fileadmin/ITWM-Media/Abteilungen/BV/Pdf/Diplomarbeit_Tesfaye.pdf
See Section 2 (Preliminaries), staring on page 3, for introduction to Rosenfeld neighbourhoods of pixels in 2D and 3D images. The adjacency relationship of neighbours of a point in summarized in Table 1, page 5.
This is good question with many possible answers, depending on a quite a number of things such as computational geometry, topology, mathematical analysis, algebra and statistics and probability theory in the analysis and representation of digital images.
One way to get started is to consider the pixels (picture elements) in a raster image. This is done, for example, using Navier-Stokes inpainting (see attached images: portrait, closeup of the eye with pixels inaccurately represented by tiny squares and eye image interpolation using Navier-Stokes inpainting) in
T. Wittman, Mathematical techniques for image interpolation:
http://www.math.ucla.edu/~wittman/thesis/Poral2.pdf
See Section 1.1, starting on page 2, for an introduction to the image interpolation problem. A good summary of the properties of an interpolated image is given on page 3. A good introduction to the statistical approach to image analysis is given in Section 6, starting on page 21.
Perhaps one of the most important studies of information in digital images was begun by A. Rosenfeld during the 1970s. It was Rosenfeld who introduced the notion of 8-neighbourhoods in digital images. Briefly, an 8-neighbourhood is defined by a particular pixel p and the 7 pixels adjacent to p. Rosenfeld's introduction of neighbourhoods of pixels ushered in the study of digital geometry and the digital topology of digital images. This subject is nicely introduced in
T.A. Aberra, Topology Preserving Skeletonization of 2D and 3D Binary Images, M.Sc. thesis, Technische Universitaet Kaiserlautern, 2004:
http://www.itwm.fraunhofer.de/fileadmin/ITWM-Media/Abteilungen/BV/Pdf/Diplomarbeit_Tesfaye.pdf
See Section 2 (Preliminaries), staring on page 3, for introduction to Rosenfeld neighbourhoods of pixels in 2D and 3D images. The adjacency relationship of neighbours of a point in summarized in Table 1, page 5.
Dear Farhad Bulbul and James F Peters,
This question and the above interesting remarks led me imediately to think of Leonardo da Vinci's quote, that «an image is worth more than a thousand words»... (What would he say about pixels, had he ever imagined that they would ever exist!)
Kind regards, Maria
Dear Maria Bettencourt Pires,
One of the outstanding features of Leonardi da Vinci's drawings and works of art (paintings and sculptures) was attention to detail. For that reason, I imagine that da Vinci would have found the implications of individual pixels in a digital image both fascinating and useful in portrayals of natural scenes.
I also think that Georges Seurat and Paul Signac anticipated the world of pixels in photographic images with their pointilistic works of art. The attached public image showing La Parade de Critique by Seurat is an example of using dots (tiny dobs of paint) to paint a picture.
Here is a list of pointillist painters--quite an amazing list:
http://www.artcyclopedia.com/history/pointillism.html
For another good example of the use of dobs in painting a scene, see Seurat's Eiffel Tower, c1889:
http://www.allposters.com/-sp/The-Eiffel-Tower-1889-Posters_i366802_.htm?aid=85097&LinkTypeID=1&PosterTypeID=1&DestType=7
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